Robust microscale structural superlubricity between graphite and nanostructured surface

Structural superlubricity is a state of nearly zero friction and no wear between two contacted solid surfaces. However, such state has a certain probability of failure due to the edge defects of graphite flake. Here, we achieve robust structural superlubricity state between microscale graphite flakes and nanostructured silicon surfaces under ambient condition. We find that the friction is always less than 1 μN, the differential friction coefficient is on the order of 10−4, without observable wear. This is attributed to the edge warping of graphite flake on the nanostructured surface under concentrated force, which eliminate the edge interaction between the graphite flake and the substrate. This study not only challenges the traditional understanding in tribology and structural superlubricity that rougher surfaces lead to higher friction and lead to wear, thereby reducing roughness requirements, but also demonstrates that a graphite flake with a single crystal surface that does not come into edge contact with the substrate can consistently achieve robust structural superlubricity state with any non-van der Waals material in atmospheric conditions. Additionally, the study provides a general surface modification method that enables the widespread application of structural superlubricity technology in atmospheric environments.


Fabrication of graphite mesa with Au cap
We fabricated square arrays of graphite mesas with an Au cap on highly ordered pyrolytic graphite (HOPG), specifically of ZYB grade (Brucker) 1 . The detailed fabrication process is depicted in Supplementary Fig. 1a. Initially, a double layer of photoresist consisting of LOR 1A (100 nm) and ZEP (400 nm) was spun onto the freshly cleaved surface of the HOPG, as illustrated in Supplementary Fig. 1a (i). Next, the photoresist in the region corresponding to the mesa pattern array was selectively removed through an electron beam lithography and development process, as depicted in Supplementary Fig. 1a (ii). Subsequently, an Au film with a thickness of 100 nm was deposited onto the surface via electron beam evaporation, as shown in Supplementary   Fig. 1a (iii). By employing a lift-off process, the Au pattern array was obtained, as illustrated in Supplementary Fig. 1a (iv). Finally, utilizing the Au pattern array as a mask, we achieved the formation of graphite mesas with an Au cap through an oxygen reactive ion etching process, as shown in Supplementary Fig. 1a (v). The etching depth was measured to be 0.8 μm.

Fabrication of nanostructured silicon surface.
In order to reproducibly fabricate uniform nanostructures on silicon surface, we produced a fabrication process as shown in Supplementary Fig. 2a. Firstly, we ultrasonically clean the silicon surface with acetone, alcohol and deionized water for 5 minutes, and then perform the surface hydrophilic treatment by oxygen plasma, as shown in Supplementary Fig. 2a (i). Then mix 200 nm polystyrene (PS) microsphere solution (mass fraction 10%, produced by Huge Biotechnology Company) with alcohol and deionized water in a ratio of 1:2:2 and ultrasonic for 30 minutes to obtain the diluted solution. Further immerse the silicon surface with deionized water and use the pipette to drop the diluted solution 250 μL, and make it self-assemble on the liquid interface, as shown in Supplementary Fig. 2a (ii).
Secondly, we evaporate the deionized water in atmospheric environment, and deposit the self-assembled PS microsphere array on the silicon surface, as shown in Supplementary Fig. 2a (iii). Then, we reduce the size of PS microspheres by oxygen plasma etching (power: 400 W, oxygen flow: 400 sccm, etching time: 4 min), as shown in Supplementary Fig. 2a (iv). In order to control the geometric size of the fabricated nanostructures, we need to accurately control the size and spacing of the PS microsphere array used as the mask, so we performed the scanning electron microscope (SEM) observation during the oxygen plasma etching process of the PS microspheres.
Supplementary Figs. 2b-d show the SEM observations of the PS microsphere array deposition, oxygen plasma etching for 3 min and 5min, respectively, and the multiples gradually increase from left to right of each image. It can be seen that the microspheres are tightly arranged on the silicon surface when they are initially self-assembled ( Supplementary Fig. 2b). After 3 minutes of oxygen plasma etching, the size of the PS microsphere array was reduced from 200nm to around 150nm ( Supplementary Fig. 2c).
When the etching time was further extended to 5 minutes, the size of the PS microsphere array was reduced to around 100 nm ( Supplementary Fig. 2d).
Thirdly, we use PS microsphere array as mask to obtain the nanostructures by ion beam etching process (beam: 1 mA/cm , energy: 500 eV, etching time: 15s), as shown in Supplementary Fig. 2a (v). It can be observed that there is still some dirt remaining on the nanostructure. Then we use acetone, alcohol, and deionized water ultrasonic cleaning to remove the residual solvents and polystyrene spheres on the nanostructures, and the AFM morphology of the fabricated nanostructured after final ultrasonic cleaning is shown in Supplementary   Fig. 2g. The nanostructures are uniformly distributed, and the peak height is uniform.
To demonstrate that solvents and polystyrene spheres were completely expelled after the fabrication of the nanostructured surface and exclude the transfer of polystyrene to the silicon surface resulting in different tribological conditions, we used a surface elemental analysis method with a shallower detection depth, that is, X-ray photoelectron spectroscopy (XPS, Thermo Fisher, Model: ESCALAB 250Xi, Source gun type: Al K Alpha, Spot size: 500 μm, Lens mode: Standard, Pass energy 30.0 eV) to characterize the prepared nanostructured silicon surface, as shown in Supplementary   Fig. 3. Supplementary Fig. 3a shows the results of the full-scan spectra (Energy step size: 1.000 eV), where the three characteristic elements of interest (C1s, O1s and Si2p) can be seen. Further, we carried out narrow scan spectra (Energy step size: 0.050 eV) for the three characteristic peaks, as shown in Supplementary Figs. 3b-d respectively.
First of all, according to the narrow scan spectra results of C1s in Supplementary Fig.   3b we measured, the peak energy is 284.82 eV, which corresponds to the adventitious hydrocarbon contamination (C aromatic and aliphatic) 2 . Compared with the standard C1s XPS spectrum features of polystyrene (Supplementary Table 1) 3 , we found that the peak at 291.27 eV corresponding to the shake-up transition does not appear in our measurement results 3,4 , which indicates that no polystyrene remains on the nanostructured silicon surface. In addition, there are two peaks in the narrow scan spectra of Si2p ( Supplementary   Fig. 3d), which are correspond to the elemental silicon and the tetravalent silicon (surface oxide layer) 2 , respectively, while the peak of O1s in Supplementary Fig. 3b corresponds to the lattice oxygen in the surface oxide layer. More detailed data about the above elements and characteristic peaks are shown in Supplementary

The transfer process of graphite flakes to the silicon surface.
After the fabrication process of graphite mesa, we need to select a graphite flake with single crystal superlubric interface and transfer to the fabricated silicon surface, and the specific process is shown in Supplementary Fig. 4, where the left and right side of each image are schematic diagram and optical microscope observation respectively.

Statistical analysis of nanostructures on silicon
In order to obtain the geometric characteristics of the fabricated nanostructures and provide a basis for subsequent simulation, we designed the following algorithm to Secondly, we get the binarization image base on Supplementary Fig. 6a with the threshold of 1 nm, as shown in Supplementary Fig. 6c. In order to locate the rough peak more accurately, we perform 4-connected erosion base on Supplementary Fig. 6c to obtain the erosion image as shown in Supplementary Fig. 6d.
Thirdly, we search for all the single connected domains in Supplementary Fig. 6d, and each domain corresponds to a rough peak. Next, we will capture the specific location and average height of each rough peak as following method. Take the i-th connected domain as an example, suppose the coordinates and height of the data points contained in it are , and ℎ 1,2,3, … , respectively. We can calculate the center coordinates , and average height ℎ of the i-th rough peak by where the height calculation considers the substrate height. The positions of all captured rough peaks , are marked with blue dots in Supplementary Fig. 6e.
Finally, we calculate the distance of the nearest rough peak for each rough peak Furthermore, we determine the shape of the rough peak to provide a basis for subsequent simulation modeling. We select a general rough peak and export its height data as shown in Supplementary Fig. 7

Friction measurement based on AFM system
Friction measurements of the graphite/n-Si heterostructures were conducted in an ambient atmosphere at a temperature of 25 ± 1 °C and a relative humidity of 30 ± 4%.
The experimental setup consisted of a commercial NTEGRA upright AFM (Cypher S-Oxford Instruments), a XYZ piezoelectric displacement platform, a high numerical aperture objective lens (×20), and a visualized AFM tip (ACCESS-NC-GG (Appnano)).
A schematic of the experimental setup is presented in Fig. 1a. To ensure precision, we carefully applied pressure to the Au cap of the graphite flake using the AFM tip, employing both the optical microscope and the piezoelectric displacement platform.
The in-situ calibration of the AFM tip was performed using the Sader method 7,8 for measuring normal direction forces and the diamagnetic levitation spring system 9 for measuring lateral direction forces. The silicon's bottom surface is securely affixed to the piezoelectric stage using tape. A photodiode captures the reflection of a laser beam projected onto the cantilever of the AFM tip, enabling precise measurement of lateral force during the sliding process by tracking the movement of the laser spot resulting from cantilever deformation.
Take the friction measurement in Fig. 2a of main text as an example, the normal force was applied by using the AFM cantilever, which can be written as , S2 where is the optical lever sensitivity, is the normal spring constant, and is optical detector signal. The lever sensitivity is measured by performing a standard force curve measurement as shown in Supplementary Fig. 8a where is the optical lever sensitivity, is the lateral spring constant of diamagnetic levitation system 9 , and is measured frictional optical detector signal 9 .
The 5.26 10 N/m was calibrated by using high-speed CCD to detect the vibration frequency of the levitate graphite sheet and precision balance to measure its mass 9 . The optical lever sensitivity was measured by using the AFM tip to drag the levitate graphite sheet and measure its lateral force curve as shown in Supplementary   Fig. 8b, we tested 256 times, and 16 of them are drawn in the figure, and we obtained its average slope 2.7003 mV/μm through linear fitting. Therefore, we calculated the lateral force coefficient / 19.48 nN/mV.

Interface characterization method for tribological experiment
Here, we provide a comprehensive description of the experimental process and methods, as illustrated in Fig. 2, Fig. 5, and Supplementary Fig. 10. Take Fig. 5 of the main text as an example, we first test the morphology of silicon sliding interface before and after friction test based on the atomic force microscope system (Cypher S-Oxford Instruments). Supplementary Fig. 9 gives a schematic diagram of the operation flow, the yellow solid block represents the graphite flake and the blue solid block represent the silicon substrate at the bottom, which includes the following steps:  Step 1: We first find the transferred graphite flake on the silicon surface through the optical microscope as shown in Supplementary Fig. 9a, and then we measure the morphology of the right area 10 μm away from the center of the graphite flake based on a piezoelectric localization system, as shown in Supplementary Fig. 9b.


Step 5: Then, we measure the morphology of the right area 10 μm away from the center of the graphite flake again after the sliding process, which contain the sliding region, as shown in Supplementary Fig. 9f.
After completing the above test process, we can continue to use the graphite flake as a mark to perform other characterization on the sliding region, such as friction mapping and Raman mapping characterization.
Supplementary Fig. 9 Interface ccharacterization process of slid silicon based on atomic force microscope system. a Prepared graphite flake/silicon heterojunction. b Step 1: Characterize the morphology 10μm 10μm silicon region centered at 10μm on the right side of the graphite flake before sliding test. After completing all the characterizations of slid silicon interface, we need to characterize the slid graphite flake interface to determine whether it occurred wear. To achieve this, we employ AB glue to lift the graphite flake, effectively overcoming the van der Waals adsorption force between the graphite flake and the silicon interface. For a comprehensive understanding of this process, please refer to the relevant references 10,11 . Subsequently, we invert the microtip by 180 degrees to enable optical microscope observations of the slid graphite flake interface, as exemplified in Fig. 2j,  Fig. 5i of the main text, and Supplementary Fig. 10j. Moreover, Raman characterization can be performed on the inverted slid graphite flake interface to determine the presence of any discernible damage, indicated by the presence of a D peak (1350 cm ).

The wear between graphite flake and atomic flat silicon surface
In order to understand the phenomenon of the large friction between the graphite flake and the atomic-level flat silicon surface in Fig. 1d of main text, we performed  Supplementary Fig. 10a is always maintained at a large level ( 5μN) throughout the process.
Secondly, we tested the 10 μm 10 μm topography of the sliding region in situ as shown in Supplementary Fig. 10b, where the white highlighted region is the graphite flake, and the yellow dash frame is the boundary of the sliding region on the silicon surface. The partial enlarged view of the upper boundary in Supplementary Fig. 10b is shown in Supplementary Fig. 11a.
Thirdly, we use the AFM tip to drag the graphite flake 6 μm to the left out of sliding region ( Supplementary Fig. 11b), and then continue to characterize the topography in situ as shown in Supplementary Fig. 10c, where the yellow dash frame is the boundary of the sliding region. There were debris on the boundary of the sliding region, but the middle topography of the sliding region as shown in Supplementary Fig.   10d is still atomically flat without any wear. We further performed the in-situ friction mapping characterization between the AFM tip and the slid silicon surface, as shown in Supplementary Fig. 11c Supplementary Fig. 11 The additional surface characterization results base on the friction test of Supplementary Fig. 10. a Partial enlarged scan of Supplementary Fig.   10b. b Move the graphite flake to the left by 6μm based on Supplementary Fig. 10b.
c Friction mapping characterization in-situ from Supplementary Fig. 10c, where the normal force applied by the AFM tip is 1 μN, and the sliding frequency is 1 Hz.
Lastly, in order to clarify the composition of wear debris, we did the Raman mapping characterization on the slid silicon surface. Supplementary Fig. 10e is the microscope observation, where the red frame area is the Raman characterization area, which contains the wear debris at the boundary of sliding region (yellow dash frame).
The intensity distributions of D peak (1350 cm ), G peak (1580 cm ) and 2D peak  Supplementary Fig. 10e) is shown in Supplementary Fig. 10i,

Van der Waals interaction in the finite element methods
The Van der Waals (vdW) interaction between the bottom surface of the graphite flake and the top surface of the nanostructured silicon substrate in the finite element methods is derived from the Lennard-Jones (LJ) potential, which is widely used to describe vdW forces between materials. The LJ potential between carbon and silicon atoms is given by:
For atoms in two surfaces in contact with coordinate , , and , , , the distance between them can be described as: , S5 in which is the distance in x-y plane. Considering that the action range of vdW forces is much smaller than the scale of the surfaces, the total potential between surfaces of unit area can be calculated as 11 : In which 1.14 10 m and 5.01 10 m are the atom number densities of carbon in graphite and silicon in substrate, ℎ is the distance between two surfaces. The pressure of vdW interaction between graphite and silicon surfaces is: The curve of function ℎ is shown as the blue line in Supplementary Fig. 12.
The balance position marked as point A takes place when ℎ 2.6 Å, and the max adhesive pressure 860MPa appears when ℎ 3.1 Å, which is marked as point B. The adhesive pressure declines rapidly as ℎ increases, and when the distance between surfaces is greater than 1 nm, the vdW interaction is negligible. The red line in Supplementary Fig. 12  (S7)) between carbon and silicon atoms. The red line is the difference approximation curve used in the finite element method.

Mesh convergence analysis
In our FEM model in Fig. 3 in main text, we used the 8-node linear hexahedral solid element with reduced integration. The number of elements is 776900, which the average size of the elements is about 20nm. In order to analyze the mesh convergence for different element numbers.

Simulation of graphite flake pressed on flat silicon surface
We performed comparative finite element method simulations of graphite flake pressed against a flat silicon substrate. The model is shown in Supplementary Fig. 14a,

Calculation of the real contact area between graphite flakes and nanostructured silicon
For finite element method model shown in Fig. 3 of main text, the pressure distribution between the bottom surface of the graphite flake and nanostructured silicon substrate can be obtained as shown in Supplementary Fig. 15. The real contact area between graphite flake and nanostructured silicon surface (i.e., the location where the pressure distribution is greater than zero) can be divided into two parts: One part is the center area of the bottom surface of the graphite flake, which is pressed on the nanostructured silicon under concentrated load; the other part is the contact area between the bottom surface of the graphite flake and some rough peaks close to the loading center.

Layer-number-dependent molecular dynamics simulations of adhesion at the graphene/silicon interface
The van der Waals interaction between the graphite and the substrate is a shortranged interaction. In our MD simulations, it is represented by Lennard-Jones potential, To validate the discussion above, we performed additional simulations with 1 and 4 layers of graphene as shown in Supplementary Fig. 17. It can be seen from the simulation results that the system using bilayer graphene already gives the saturated value of adhesion.

Analyse of the water film at the nanostructured surface
The contacts used in our experiments are composed of graphite and silicon surface.
When exposed to ambient condition, e.g., the temperature of 25 ± 1 °C and relative humidity of 25± 1% as used in our experiment, the graphite will be covered with a water film of which the thickness is less than 1 nm 13 . For the silicon surfaces, there have also been detailed experimental measurements which shows that the thickness of the water film is also less than 1 nm [14][15][16]

General surface modification methods for superlubric generators (SLGs) application scenarios
The surface modification method employed in this work provides a general surface modification method to achieve robust structural superlubric (SSL) state between graphene flakes and non-vdW materials, which promote the general application of SSL technology. For example, as an application of SSL, several types of superlubric generators (SLGs) have been proposed 10,20 . SLG is designed to produce stable high current density and long-lifespan output under relative sliding through SSL technology, and the conversion efficiency is close to 100% 10,20 . Recently, the Schottky superlubric generator (S-SLG), that is, the sliding contact between micro-sized graphite flakes and n-type silicon in the SSL state, was proposed as a physical prototype of SLGs ( Supplementary Fig. 19a), which can not only generate a stable and high current density of ~210Am and power density of ~7 Wm , but more importantly, achieve a long lifetime of at least 5,000 cycles while maintaining stable high electrical current density (~119 Am ) 10 .
However, the edges of graphite flake will cause high friction and wear with a certain probability, leading to the failure of the SLG, as shown in Supplementary Fig.   19a. Here, we demonstrate our surface modification method to optimize the original SLG to avoid high friction and wear, as shown in Supplementary Fig. 19b. The nanostructures are prepared on the n-Si surface, so that the edge of the graphite flake is warped under the central loading to avoid high friction and wear that may occur at graphite flake edges and form a robust SSL state. To promote SLG to large-scale batch applications, we can connect the centers of multiple graphite flakes placed on nanostructured n-Si with columnar Ni through sacrificial layer and electroplating methods to realize the center loading (inducing warpage curved edges) and integrated connections of surface-modified SLGs, as shown in Supplementary Fig. 19c. While the microfabrication process of such structure is under operation and takes time, we believe that with the mechanism revealed in our present manuscript, it is reasonable to believe that the friction and wear will greatly be reduced with the help of edge warping.
Supplementary Fig. 19 Optimized superlubric generators (SLGs) through surface modification. a Schematic diagram of original SLG, the graphite flake and n-Si form a structural superlubric (SSL) contact, which will produce stable high current density and long-lifespan output under relative sliding, but the edges will cause high friction and wear with a certain probability. b Schematic diagram of surface-modified SLG, nanostructures are prepared on the n-Si surface, so that the edge of the graphite flake is warped under the central loading to avoid high friction and wear that may occur at graphite flake edges and form a robust SSL state. c Assembly of surface-modified SLGs, the centers of multiple graphite flakes placed on nanostructured n-Si are connected with columnar nickel by sacrificial layer and electroplating methods, realizing the functions of center loading (inducing warped edges for robust SSL) and integrated connection to promote SLG towards large-scale batch application.